Branching processes can be seen all around us. Branching geometry provides free standing trees, plumbing and electricity in buildings, electric current through branched wiring, and lightening fractures through the air in dendrites. Our lungs breathe air in to be absorbed by branching bronchioles and alveoli, which cover an enormous surface of over 100 m2. On that surface gases are exchanged to our branching blood vessels to be carried to and from our cells. Our extraordinary branched circulatory system reaches all of our cells, but itself is a small fraction of our body's volume.
While there are innumerable examples of the value of branching to distribute fluid, provide structural support, optimize surface area to volume ratio, etc., the formation of branched structures is tedious. Biology often uses branched channel pathways to distribute fluid to surfaces. By comparison, our own manufacturing methods are inefficient.
As an example, NASA's Liquid Cooling and Ventilation Garment is designed to circulate coolant to the surface of the human body. It achieves this by snaking 48 individual tubes of a combined length of over 90 meters through a fabric garment in a serpentine pattern. The many manifolds required are cumbersome, as is the hosing. The process of manufacturing these suits has changed little since the Apollo mission, and involves the tedious sewing of the tubing into the garment.
Another method is currently used to produce branched channels in silicone for head cooling caps to prevent hair loss in chemotherapy patients. It involves the creation of a master mold, the casting of two separate membranes, and the lamination of the two membranes to close the channels. It is a time intensive process.
Another method currently makes use of 3D printing to create branched channels. Indeed, 3D printing is able to produce bodies with embedded hollow channel networks in a single print. However, this is a time intensive process, with each “voxel” of material needing to be added in series. It is highly limited to materials, and ill-suited to rapidly produce customized channel networks in a soft, wearable material.
It is the natural propensity of less viscous fluids to branch, when forced into more viscous fluids, while constrained to a quasi-two-dimensional space. This is a process known as viscous fingering. By controlling the geometry of that space, one can control the pressure gradients that dictate the growth of branched channels.
Viscous fingering has been studied as an experimental process since 1958. The process has been investigated by science laboratories studying pattern formation. Most of the literature describes various physical characteristics of the fluid flow within Hele-Shaw cells.
In a study entitled Self-Patterned Growth of Branched Structures in Non-Curing and in Curable Structures via Electro-Hydrodynamic Hele-Shaw Flow, Drexel University (2009), an applied electrical field was used to control the branching of channels in a curable medium. This method limits the use of viscous fingering to a subclass of dielectric host fluids and conductive guest fluids. It hampers rapid customization of channel geometry by using electrodes to direct and stabilize channel growth.
Another study entitled, A practical method for patterning lumens through ECM hydrogels via viscous finger patterning, J. Lab. Automation (2012) does not take advantage of the branching. Instead, the tunneling process is used to hollow out pre-made tubular forms and leave a coating with a biomimetic lumen texture. This application lacks a self-organizing fluidic process that is controllable and compatible with design.
It has been of interest to investigate the phenomenon of viscous fingering for the purpose of increasing yields in oil well extraction. CN 104268401 (A) provides a method for simulating the fluidic process in a porous medium and analytical systems used in researching the viscous fingering of fractured acidification construction in an oil field. In the art of oil well extraction, viscous fingering is a phenomenon that is sought to be reduced, rather than employed in useful contexts.
A version of the fluidic process has been used to produce a unique identifying mark for the purposes of security, DE 102012010482, (A1) 2012, and similarly to produce a structured coating in WO2007030952 (A1), 2007. However, neither of these inventions discloses a method to create closed channel structures out of the fluidic process. For this reason, they fail to realize the full potential of the branched-pattern formation process.
A melt stretching process KR20140043740 (A)—2014 makes use of randomly distributed drops of liquid plastics to build random reinforcement between laminar sheets. However, this process falls short of an ability to design and control the growth of channel building processes into intentionally shaped branched systems.
The fractal properties of the viscous fingering phenomenon offer many unique and valuable applications. Whereas it is often of great value to create a fractal distribution of matter (in flow pipes CN104806489, (A) 2015, in antennas CN103311663 (A)—2013, in heat exchangers CN101932899 (A)—2010, and spreading structures JP2007022171 (A)—2007) the methods for manufacturing such structures are not designed with this end goal in mind. Methods for entrenching fractal channels may involve casting molds, connecting pipes, CNC milling, 3D printing, laser etching, electrical discharge machining, photolithography, and the like, but none of these methods is capable of rapidly building an enclosed branched-channel network. Thus there is a need for an efficient and cost-effective system and method to produce branched structures with practical applications using a process known as viscous fingering.